I prune mine back a lot, but not to the ground. Like any shrub you need to leave enough stem so there is something to set buds.

My thyme's only a year old and about 3 inches tall. Advice on pruning please? I've never pruned anything.

3" tall? I'm assuming it's made a mat. Just sheer off the ends, which probably look a little ragged and bare anyway. How about a little fertilizer? Just a little tho'.

I have both creeping and upright Thyme's and always wait until I see new growth and then prune back just above this. This year my German Winter acted evergreen and since I pruned them nicely last fall so I won't again until I need shear back flowers...late spring when I will prune back pretty hard.
The Creeping Thyme (T. serypllum) was a little ragged looking... new growh was emerging from beneath and I just finished pruning it all back to this.
Upright Thyme does much better when regularily harvested or sheared back throughout the season...I haven't had any woody plants in the 3 years I've had them.

Vera

Prune in early summer following the blooming phase.

Prune in late fall to remove long woody stems.

Shape prune whenever, but definitely do a spring clean prune to remove dead areas and to shape the plant.

Herbs like haircuts

My Thyme grows upright. I have never be able to properly ID it. I prune hard in late spring. It is in the process of being trained as bonsai.